Overlapping cohorts are of critical importance in substance abuse research. The application of latent curve analysis (LCA) to the study of change in overlapping cohorts has become popular, yet potential problems with this new modeling paradigm have received relatively little scrutiny. If the fundamental assumption of invariance fails to hold, observed differences over time may be due to changes in measurement and not to changes in the construct itself. Despite its importance, longitudinal invariance is not well understood analytically and is rarely evaluated empirically, increasing the risk that invalid conclusions might be drawn from LCA applied to empirical data. Given the critical role invariance plays in LCA, this will be the focus of the proposed project. The project is organized around three central aims. Aim 1 is to review and integrate the literature on factorial invariance, with an emphasis on cohort-sequential LCA. Aim 2 will draw upon the results of Aim t to inform the design and implementation of a computer simulation to empirically study measurement invariance in cohort-sequential designs under conditions commonly encountered substance use research. Aim 3 is to synthesize the findings of Aims 1 and 2 and apply them to empirical data sets studying the relation between stress and substance use in children of alcoholics.